报告题目： Environment Invariant Generalized Linear Model: Theory and Algorithm

报 告 人：孔令臣 教授（北京交通大学）

报告时间：2026年9月11日（星期五）14:20—15:00

报告地点：数学科学学院114（小报告厅）

校内联系人：吴佳 教授         联系方式：84708351-8415

报告摘要： Learning invariant predictive relationships across heterogeneous environments is crucial for out-of-distribution (OOD) generalization and stable feature identification. In this work, we study a sparse environment-invariant generalized linear model (EIGLM) and formulate its estimator with an explicit sparsity constraint. From a statistical perspective, we establish that the population objective uniquely identifies the true invariant parameter, and we derive non-asymptotic estimation error bounds together with support recovery consistency guarantees in high-dimensional regimes. From a computational perspective, we reformulate the estimator as a sparsity-constrained binary integer program and introduce a sharp-peak penalty function. We prove an exact penalty theorem, demonstrating that the penalized formulation is equivalent to the original mixed-integer model beyond a solution-independent threshold; furthermore, we characterize first-order optimality via P-stationarity. We then develop an alternating proximal gradient descent algorithm with closed-form proximal updates, establishing subsequence convergence, finite-step binary identification, global sequence convergence, and linear convergence rates under mild assumptions. Extensive numerical experiments on both synthetic and real-world datasets demonstrate the effectiveness of the proposed method in identifying invariant and causal variables while maintaining competitive predictive accuracy.

报告人简介：孔令臣，北京交通大学教授，博士生导师，中国运筹学会数学规划分会理事长，中国运筹学会组织委员会副主任。主要从事对称锥互补问题和最优化、高维数据分析、统计优化与学习及其应用等方面的研究。在《Mathematical Programming》《SIAM Journal on Optimization》《IEEE Transactions on Pattern Analysis and Machine Intelligence》《IEEE Transactions on Signal Processing》《Technometrics》《Statistica Sinica》《Electronic Journal of Statistics》等期刊发表论文100余篇。主持国家重点研发计划、国家自然科学基金重点项目、国家自然科学基金面上项目等10余项。2012年获中国运筹学会青年奖，2018年获得北京市高等教育教学成果一等奖，2022年获教育部自然科学二等奖等。